| 局部射影平坦且具有迷向S 曲率的两类重要的芬斯勒度量 |
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| 引用本文： | 蒋经农,冯 伟.局部射影平坦且具有迷向S 曲率的两类重要的芬斯勒度量[J].西南农业大学学报,2012,34(6):101-104. |
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| 作者姓名： | 蒋经农 冯 伟 |
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| 作者单位： | 遵义医学院医学信息工程系 |
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| 基金项目： | 贵州省科学技术基金资助项目(黔科合体R字[2011]2006号) |
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| 摘 要： | 研究了两类重要的分别形如F=αekβ/α和F=α+εβ+2kβ2/α-k2β4/3α3的芬斯勒度量,其中k≠0,ε为常数,α=((aij(x)yiyj)～(1/2))为黎曼度量,β=bi(x)yi为流形上的1-形式.得到了它们为局部射影平坦度量且具有迷向S-曲率的充要条件.
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| 关 键 词： | 芬斯勒度量 射影平坦的芬斯勒度量 S-曲率 (α β)-度量 |
TwoImportantClassesofLocallyProjectively
FlatFinslerMetricswithIsotropicS-Curvature |
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| JIANG Jing-nong,FENG Wei.TwoImportantClassesofLocallyProjectively
FlatFinslerMetricswithIsotropicS-Curvature[J].Journal of Southwest Agricultural University,2012,34(6):101-104. |
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| Authors: | JIANG Jing-nong FENG Wei |
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| Institution: | Department of Medical Information Engineering,Zunyi Medical College,Zunyi Guizhou 563000,China |
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| Abstract: | Two important classes of Finsler metrics in the forms of F=αekβ/α and F=α+εβ+2kβ2/α-k2β4/3α3 are considered,where k≠0,ε are constants,α=((aij(x)yiyj)～(1/2)) is a Riemannian metric,and β=bi(x)yi is a 1-form on a manifold.The sufficient and necessary conditions for them to be locally projectively flat and of isotropic S-curvature are obtained. |
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| Keywords: | Finsler metric projectively flat Finsler metric S-curvature (α β)-metric |
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